Problem: $ E = \left[\begin{array}{rr}2 & -1 \\ 4 & -1 \\ 0 & 4\end{array}\right]$ $ D = \left[\begin{array}{rrr}4 & 0 & 2 \\ 4 & 0 & -2 \\ 0 & 4 & 0\end{array}\right]$ Is $ E+ D$ defined?
In order for addition of two matrices to be defined, the matrices must have the same dimensions. If $ E$ is of dimension $( m \times  n)$ and $ D$ is of dimension $( p \times  q)$ , then for their sum to be defined: 1. $ m$ (number of rows in $ E$ ) must equal $ p$ (number of rows in $ D$ ) and 2. $ n$ (number of columns in $ E$ ) must equal $ q$ (number of columns in $ D$ Do $ E$ and $ D$ have the same number of rows? Yes Yes No Yes Do $ E$ and $ D$ have the same number of columns? No Yes No No Since $ E$ has different dimensions $(3\times2)$ from $ D$ $(3\times3)$, $ E+ D$ is not defined.